Al-Shabab fighters in northern Mogadishu, Somalia. Kenyan military forces moved into southern Somalia on Sunday, an official said. Photograph: Farah Abdi Warsameh/AP

Kenyan military forces moved into southern Somalia on Sunday, officials and residents said, a day after Kenyan defence officials said the country has the right to defend itself after a rash of militant kidnappings of Europeans inside Kenya.

Residents in southern Somalia said that columns of Kenyan troops had moved in and that military aircraft were flying overhead. Ali Nur Hussein said Kenyan troops arrived in tanks and trucks, and were co-ordinating with Somali government soldiers.

Kenya's government spokesman, Alfred Mutua, said Kenyan troops "are pursuing al-Shabab across the border." He did not give any other details.

In response, al-Shabab, Somalia's most dangerous militant group, tried to raise the alarm in areas it controls. Residents in the town of Qoqani who asked not to be named for fear of reprisals said militants were going into homes and forcibly recruiting new fighters.

"Are you ready to live under Christians?" one al-Shabab official shouted on a militant radio station. "Get out of your homes and defend your dignity and religion. Today is the day to defend against the enemy."

A Somali government spokesman, Abdirahman Omar Osman, said his government welcomes logistical support from "our Kenyan brothers," but said Somalia did not need Kenyan troops.

"Our forces are ready to combat al-Shabab and they are doing so effectively. They are ready at the borders, so sending troops is not needed," Osman said.

Kenyan troops have frequently crossed the border into Somalia, but Sunday's push appears to be a bigger and more concerted effort. Minister of internal security George Saitoti told a news conference on Saturday that Kenyan forces would pursue al-Shabab into Somalia.

"For the first time our country is threatened with the most serious level of terrorism," he said.

The public declaration to attack al-Shabab came two days after armed militants kidnapped two Spanish aid workers with the group Doctors Without Borders from the Dadaab refugee camp, a sprawling expanse of temporary homes where almost 500,000 Somalis live. The population of Dadaab, the world's largest refugee camp, has swelled by tens of thousands in recent months because of Somalia's famine.

On 1 October, Somali gunmen took a wheelchair-bound Frenchwoman from her home near the resort town of Lamu. Somalis also abducted a British woman from a Kenyan coastal resort in September. Her husband was killed in the attack.

Kenya's push north into Somalia will open another front that Somali militants must contend with. African Union forces from Uganda and Burundi have expanded their control of Mogadishu in recent months and have almost completely forced al-Shabab out of the capital.